Effects of a parametric perturbation in the Hassell mapping. (August 2018) - de Oliveira, Juliano A.; de Mendonça, Hans M.J.; da Costa, Diogo R.; Leonel, Edson D.
Highlights: In this work we investigate the effects of a parametric perturbation in the dynamical properties of the Hassell mapping. We analyze the convergence to the fixed point as well as to characterize the organization of the extreming curves in the parameter space. We consider scaling laws to investigate the convergence to the asymptotic state. The extreming curves in the parameter space dictates the organization for the windows of periodicity therefore demonstrating how the set of shrimp-like structures are organized. Abstract: The convergence to the fixed point near at a transcritical bifurcation and the organization of the extreming curves for a parametric perturbed Hassell mapping are investigated. The evolution of the orbits towards the fixed point at the transcritical bifurcation is described using a phenomenological approach with the support of scaling hypotheses and homogeneous function hence leading to a scaling law related with three critical exponents. Near the bifurcation the decay to the fixed point is exponential with a relaxation time given by a power law. The extreming curves in the parameter space dictates the organization for the windows of periodicity, consequently demonstrating how the set of shrimp-like structures are organized.